What is the integral of cos(y)sin(y)+y^2 ?

The integral of cos(y)sin(y)+y^2 is (sin^2(y))/2+(y^3)/3+C

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integral of cos(y)sin(y)+y^2

\int cos (y) sin (y) + y^{2} d y

\frac{sin ^{2} ( y )}{2} + \frac{y ^{3}}{3} + C

Solution steps

\int cos (y) sin (y) + y^{2} d y

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int cos (y) sin (y) d y + \int y^{2} d y

\int cos (y) sin (y) d y = \frac{sin ^{2} ( y )}{2}

\int y^{2} d y = \frac{y ^{3}}{3}

= \frac{sin ^{2} ( y )}{2} + \frac{y ^{3}}{3}

Add a constant to the solution

= \frac{sin ^{2} ( y )}{2} + \frac{y ^{3}}{3} + C

What is the integral of cos(y)sin(y)+y^2 ?
The integral of cos(y)sin(y)+y^2 is (sin^2(y))/2+(y^3)/3+C